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<h1 align=center> Axiom 3: Functional Equation
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There exist numbers $Q>0$, $\alpha_j>0$, and $\Re(r_j)\ge 0$,
such that
$$
\Phi(s):= Q^s \prod_{j=1}^d \Gamma(\alpha_j+r_j) F(s) 
$$
satisfies
$$
\Phi(s)=\varepsilon {\overline{\Phi}}(1-s).
$$
Here $|\varepsilon|=1$ and 
${\overline{\Phi}}(z)={\overline{\Phi({\overline{z}})}}$.\begin{rawhtml}
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Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
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